Department of Applied Mathematics, School of Mathematics, University of Leeds, Leeds, United Kingdom.
CBR Division, Defence Science and Technology Laboratory, Salisbury, United Kingdom.
Front Immunol. 2021 Aug 23;12:688257. doi: 10.3389/fimmu.2021.688257. eCollection 2021.
We present a stochastic mathematical model of the intracellular infection dynamics of in macrophages. Following inhalation of spores, these are ingested by alveolar phagocytes. Ingested spores then begin to germinate and divide intracellularly. This can lead to the eventual death of the host cell and the extracellular release of bacterial progeny. Some macrophages successfully eliminate the intracellular bacteria and will recover. Here, a stochastic birth-and-death process with catastrophe is proposed, which includes the mechanism of spore germination and maturation of . The resulting model is used to explore the potential for heterogeneity in the spore germination rate, with the consideration of two extreme cases for the rate distribution: continuous Gaussian and discrete Bernoulli. We make use of approximate Bayesian computation to calibrate our model using experimental measurements from infection of murine peritoneal macrophages with spores of the Sterne 34F2 strain of . The calibrated stochastic model allows us to compute the probability of rupture, mean time to rupture, and rupture size distribution, of a macrophage that has been infected with one spore. We also obtain the mean spore and bacterial loads over time for a population of cells, each assumed to be initially infected with a single spore. Our results support the existence of significant heterogeneity in the germination rate, with a subset of spores expected to germinate much later than the majority. Furthermore, in agreement with experimental evidence, our results suggest that most of the spores taken up by macrophages are likely to be eliminated by the host cell, but a few germinated spores may survive phagocytosis and lead to the death of the infected cell. Finally, we discuss how this stochastic modelling approach, together with dose-response data, allows us to quantify and predict individual infection risk following exposure.
我们提出了一个描述 感染巨噬细胞的细胞内动力学的随机数学模型。 孢子被吸入后,被肺泡吞噬细胞吞噬。然后,吞噬的孢子开始在细胞内发芽和分裂。这可能导致宿主细胞最终死亡,并将细菌后代释放到细胞外。一些巨噬细胞成功地消灭了细胞内的细菌并恢复了健康。在这里,我们提出了一个带有灾变的随机生灭过程,其中包括孢子发芽和 成熟的机制。所得到的模型用于探索孢子发芽率的异质性的潜力,考虑了发芽率分布的两种极端情况:连续高斯和离散伯努利。我们利用近似贝叶斯计算方法,使用来自 34F2 菌株的 孢子感染鼠腹膜巨噬细胞的实验测量数据对模型进行校准。校准后的随机模型使我们能够计算已被一个孢子感染的巨噬细胞破裂的概率、破裂的平均时间和破裂大小分布。我们还获得了一段时间内细胞群体中孢子和细菌的平均负荷,假设每个细胞最初都被一个孢子感染。我们的结果支持发芽率存在显著的异质性,预计一小部分孢子会比大多数孢子晚得多发芽。此外,与实验证据一致,我们的结果表明,巨噬细胞摄取的大多数孢子可能被宿主细胞消除,但一些发芽的孢子可能在吞噬作用后存活下来,并导致感染细胞的死亡。最后,我们讨论了这种随机建模方法如何结合剂量-反应数据,使我们能够量化和预测暴露后个体感染的风险。